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(June 30, 2021)

Where analytic gradients are not available, static polarizabilities (only) can
be computed via finite-difference in the applied field, which is known as the
*finite field* (FF) approach. Beginning with Q-Chem 5.1, a
sophisticated “Romberg” approach to FF differentiation is available, which
includes procedures for assessing the stability of the results with respect to
the finite-difference step size. The Romberg approach is described in
Section 10.13.2. This section describes Q-Chem’s older approach
to FF calculations based on straightforward application of small electric
fields along the appropriate Cartesian directions.

Dipole moments can be calculated numerically as the first derivative of the energy with respect to $\overrightarrow{F}$ by setting JOBTYPE = DIPOLE and IDERIV = 0. If IDERIV is not specified explicitly, the dipole moment will be calculated analytically, which for post-Hartree–Fock levels of theory invokes a gradient calculation in order to utilize the relaxed wavefunction.

Similarly, set JOBTYPE = POLARIZABILITY for numerical evaluation of the static polarizability tensor $\overleftrightarrow{\alpha}$. This is performed by either first-order finite difference, taking first-order field derivatives of analytic dipole moments, or by second-order finite difference of the energy. The latter is useful (indeed, required) for methods where analytic gradients are not available, such as CCSD(T) for example. Note, however, that the electron cloud is formally unbound in the presence of static electric fields and therefore a bound solution is a consequence of using a finite basis set. (With analytic derivative techniques the perturbing field is infinitesimal so this is not an issue.) This fact, along with the overall sensitivity of numerical derivatives to the finite-difference step size, means that care must be taken in choosing the strength of the applied finite field.

To control the order for numerical differentiation with respect to the applied
electric field, use IDERIV in the same manner as for geometric
derivatives, *i.e.*, for polarizabilties use IDERIV = 0 for second-order
finite-difference of the energy and IDERIV = 1 for first-order finite
difference of gradients. In addition, for numerical polarizabilities at the
Hartree-Fock or DFT level set RESPONSE_POLAR = $-1$ in order to disable
the analytic polarizability code.

RESPONSE_POLAR

Control the use of analytic or numerical polarizabilities.

TYPE:

INTEGER

DEFAULT:

0 or $-$1
= 0 for HF or DFT, $-$1 for all other methods

OPTIONS:

0
Perform an analytic polarizability calculation.
$-$1
Perform a numeric polarizability calculation even when analytic 2nd derivatives are available.

RECOMMENDATION:

None

In finite-difference geometric derivatives the *$rem* variable
FDIFF_STEPSIZE controls the size of the nuclear displacements but
here it controls the magnitude of the electric field perturbations:

FDIFF_STEPSIZE

Displacement used for calculating derivatives by finite difference.

TYPE:

INTEGER

DEFAULT:

1
Corresponding to $1.88973\times {10}^{-5}$ a.u.

OPTIONS:

$n$
Use a step size of $n$ times the default value.

RECOMMENDATION:

Use the default unless problems arise.